Kinetics of the Reaction of OH with Isoprene over a Wide Range of

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A: Kinetics, Dynamics, Photochemistry, and Excited States

Kinetics of the Reaction of OH with Isoprene over a Wide Range of Temperature and Pressure Including Direct Observation of Equilibrium with the OH Adducts Diogo J Medeiros, Mark A. Blitz, Leanne James, Thomas Speak, and Paul W. Seakins J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b04829 • Publication Date (Web): 23 Aug 2018 Downloaded from http://pubs.acs.org on August 24, 2018

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The Journal of Physical Chemistry

Kinetics of the Reaction of OH with Isoprene over a Wide Range of Temperature and Pressure Including Direct Observation of Equilibrium with the OH Adducts D.J. Medeiros,1 M.A. Blitz,*1,2 L. James,1 T.H. Speak,1 P.W. Seakins*1,2 1 - School of Chemistry, University of Leeds, Leeds, LS2 9JT, UK. 2 – National Centre for Atmospheric Science, University of Leeds, Leeds, LS2 9JT, UK. Abstract The reaction of the OH radical with isoprene, C5H8 (R1), has been studied over the temperature range 298 - 794 K and bath gas pressures of nitrogen from 50 - 1670 Torr using laser flash photolysis (LFP) to generate OH, and laser induced fluorescence (LIF) to observe OH removal. Measurements have been made using both a conventional LFP/LIF apparatus and a new high pressure system. The measured rate coefficient at 298 K (k1,298 K = 9.90 ± 0.09) × 10-11 cm3 molecule-1 s-1) in the high pressure apparatus is in excellent agreement with the literature confirming the accuracy of measurements made with this instrument. Above 700 K, the OH decays were no longer single exponentials due to regeneration of OH from adduct decomposition and the establishment of the OH + C5H8 ⇌ HOC5H8 equilibrium, R1a/R-1a. This equilibrium was analysed by comparison to a master equation model of reaction R1, and determined the well-depth for OH addition to carbon C1 and C4 to be equal to (153.5 ± 6.2) kJ mol-1 and (143.4 ± 6.2) kJ mol-1, respectively. These well-depths are in excellent agreement with the present ab initio - CCSD(T)/CBS//M062X/6-311++G(3df,2p) – calculations (154.1 kJ mol-1 for the C1 adduct). Addition to the less stable C2 and C3 adducts are not important. The data above 700 K also indicated that a minor, but significant direct abstraction channel, R1b, was also operating with k1b = (1.3 ± 0.3) × 10-11 exp

-3.61 kJ mol-1 RT

cm3 molecule-1 s-1.

Additional support for the presence of this abstraction channel comes from our ab initio calculations and from room-temperature proton transfer mass spectrometry product analysis. The literature data on reaction R1 together with the present data were assessed using master equation analysis, using the MESMER package. This analysis produced a refined dataset that generates our recommended k1a(T,[M]). An analytical representation of k1a(T,[M]) and k-1a(T,[M]) is provided via a Troe expression. The reported experimental data (the sum of addition and abstraction), -11 k∞ 298 K 1 = (9.5 ± 0.2) × 10 T

-1.33 ± 0.07

+ (1.3 ± 0.3) × 10-11 exp

s-1, significantly extends the measured temperature range of R1.

1 ACS Paragon Plus Environment

-3.61 kJ mol-1 RT

cm3 molecule-1

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*Authors to whom correspondence [email protected] .

should

be

addressed.


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[email protected],

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1 Introduction The diene isoprene, C5H8, is the dominant biogenic hydrocarbon emission.1-2 Isoprene reacts rapidly with the OH radical (R1, k298 K = (1.00 ± 0.15) × 10-10 cm3 molecule-1 s-1)3 and, in the presence of NOx, can lead to significant local air quality issues, particularly ozone formation.4 OH + C5H8 → Products

(R1)

In low NOx/high isoprene environments such as forests, where there is a rapid loss route for OH with isoprene, but no obvious route for OH regeneration, it was expected that ambient [OH] would be low. However, campaigns in a variety of such environments ranging from boreal forests5 to Mediterranean pine forests,6 to rain forests7-8 have measured surprisingly high concentrations of OH, with the measured:modelled [OH] being up to 10:1.7 These observations suggest a mechanism for OH regeneration; the implications of a higher concentration of ambient OH on methane lifetimes, and hence on radiative forcing, are significant.9 A range of mechanisms10 including OH production from RO2 + HO2 reactions11, RO2 photolysis12 and epoxide formation from OH + isoprene adducts13 have been investigated. These processes provide some enhancement of OH levels, but do not bridge the gap between measurement and model. Currently the most promising mechanism for explaining OH regeneration is the Leuven Isoprene Mechanism (LIM), proposed by Peeters and coworkers.14-15 Under low NOx conditions the OH-isoprene-O2 radical formed in reactions R1aR2, can isomerize to form a hydroperoxycarbonyl (HPALD) / dihydroperoxycarbonyl (diHPCARP) species that lead to OH regeneration. OH + C5H8 → HOC5H8

(R1a)

HOC5H8 + O2 → HOC5H8O2

(R2)

The reactions of HOC5H8O2 take place on minute/hour timescales at room temperature and it is difficult, even with the most careful experiments, to eliminate the possibility of contributions from heterogeneous processes or secondary chemistry. Additionally, in some chambers it is not possible to avoid a contribution from NOx driven chemistry,16 so the resulting product distribution can be complex and identifying the products from low NOx chemistry can be difficult. However, given the importance of quantifying the HOx budget in tropical regions, quantitative validation of the role of the LIM115 mechanism is required. An alternative approach to mechanism validation is to use direct techniques at higher temperatures to observe OH regeneration (via HOC5H8O2 isomerization for isoprene oxidation) on millisecond timescales in flash photolysis experiments.17 Under these conditions there can be no contribution from heterogeneous processes and NOx can be rigorously excluded. However, to drive the isomerization chemistry to the millisecond timescale, high temperatures must be used and this has a consequent effect in the high concentration of oxygen required to ensure a substantial concentration of HOC5H8O2 as reaction R2 reaches equilibrium conditions. The resulting high pressures and concentrations 3 ACS Paragon Plus Environment


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of O2 make conventional observation of OH by laser induced fluorescence (LIF) difficult, due to quenching of the fluorescence signal. However, we have recently developed a new high pressure flash photolysis reactor based on the FAGE technique, where OH is sampled into a low pressure region before detection by LIF,18 such that measurements can be made under these conditions. Reaction R1, at least at low temperatures (C1=C2< double bond in the isoprene structure has a single-bond analogue in the product structure, which provides an augmented torsional degree of freedom to the molecule, with respect to this bond. Figure 1 shows all the torsions that were described with the hindered rotor approximation for both isoprene and the two most stable isoprene-OH adducts considered in the analysis. The descriptions of these hindered rotors were obtained through 360° relaxed scans of the dihedral angle respective to the specific rotation, with steps of 15°. Restricted optimizations at the M06-2X/6-311++G(3df,2p) level were applied at each step. In order to avoid inconsistency in the number of degrees of freedom of species in the ME calculations, the description of a hindered rotor requires the removal of a corresponding vibrational frequency. MESMER uses the projection method proposed by Sharma et al.41 to define the mode related to the internal rotation. Pressure dependent reactions can be modelled with the ME method.42-43 The energies of the reagents and C5H8-OH adducts are divided into grains, a typical grain width being ~ 50 cm-1; a series of coupled differential equations then links the energy grains of the adduct. Each grain can be populated or de-populated by collisional energy transfer into another energy grain of the adduct, additionally each grain can also be populated by the pseudo-firstorder chemical reaction of OH and isoprene and de-populated by re-dissociation to reagents. The probability of energy transfer between grains i,j is determined by the exponential down model (i.e. the probability decreases exponentially dependent on the energy separation between i and j) with reverse probabilities determined by detailed balance. The energy transfer parameter d,M is given by d,M = Ad,M × (T/298)m, being its temperature dependence, m, fixed to typical values according to the implemented bath gas (1.00, 0.30 and 0.25 for He, Ar and N2 respectively).23 The limited pressure dependence observed in the temperature range covered by this investigation would prevent a precise estimate of this parameter. Ad,M depends on the bath gas used, however, it is possible to assign different values to each bath gas and hence to compare experimental studies using different bath gases. The microcanonical, energy dependent, rate coefficients, k(E), linking reagents and adducts are related to the thermal rate coefficients via an inverse Laplace transformation. In general terms, the energy grained master equation (EGME) can be described as: dp = Mp dt

E3 8 ACS Paragon Plus Environment

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where p is the population density vector and M, the transition matrix, describes the evolution of the population over time due to reaction and collisional energy transfer. The solution of E3 yields:

p = UeΛt U−1 p(0)

E4

where U is a matrix of eigenvectors obtained by the diagonalization of M, Λ is the vector or corresponding eigenvalues and p(0) contains the initial conditions for each grain. MESMER solves the EGME and extracts the phenomenological rate coefficients from the chemically significant eigenvalues. The selection of these eigenvalues is made by the procedure described by Bartis and Widom.44 Information on parameters used can be found in an example MESMER script in the Supplementary Information.

3 Data Analysis 3.1 Single Exponential Traces At temperatures below 650 K, OH reacted under pseudo-first-order conditions via a simple removal process; in this regime, the concentration of OH as a function of time is given by: '

[OH]t =[OH]0 e-k1t

E5

where k1' is the pseudo-first-order rate coefficient given by: k1' = k1[C5H8] + k1st

E6

Here k1 is the bimolecular rate coefficient for reaction R1 and k1st represents the rate coefficient for the loss processes due to diffusion and reaction of OH with the constant concentration of precursor, kp. As the OH LIF signal is proportional to [OH], the [OH] in E5 can be replaced by the OH LIF signal and the resulting exponential fit (inset to Figure 2) to the LIF data, returns k1'. Under these conditions, a plot of k1' vs [C5H8] should give a straight line, as shown in Figure 2, where the gradient is k1 and the intercept is the sum of the first order loss processes. The resulting k1 rate coefficients are summarised in Table 1. Table 1. Experimental Determinations of k1 from Single Exponential Decays T/K

p / Torr

298 298 298 298 337 406 417 418 426

1290 1365 96b 56 57 1367 1497 1418 103

k1 × 1011 / cm3 molecule-1 s-1 a 9.90 ± 0.14 10.01 ± 0.12 10.60 ± 0.36 10.40 ± 0.32 8.28 ± 0.22 6.68 ± 0.54 7.2 ± 1.6 6.24 ± 0.34 5.56 ± 0.26

T/K

p / Torr

473 475 477 478 508 533 540 564 573

99 1394 128 114 1673 132 141 1350 51 9

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k1 × 1011 / cm3 molecule-1 s-1 a 4.98 ± 0.36 5.61 ± 0.50 5.3 ± 1.0 6.12 ± 0.36 5.7 ± 1.2 4.91 ± 0.24 5.27 ± 0.36 4.74 ± 0.44 4.4 ± 1.1


433 472

1546 99

6.0 ± 1.5 5.81 ± 0.86

618 630

1536 1373

3.99 ± 0.46 4.71 ± 0.56

a – Errors are 2σ. b – Data where p725 K and p ~ 100 Torr.

4 Results and Discussion 4.1 Ab initio calculations Figure 5 shows the potential energy surface for OH addition and H-abstraction from isoprene at the CCSD(T)/CBS//M06-2X/6-311++G(3df,2p) level. OH addition to C2 or C3 carbons produces adducts with significantly higher energies as there is no allylic stabilization of the resulting radicals. The energy difference between the C1 and C4 adducts is approximately 10 kJ mol-1 (in good agreement with previous literature, see Table 3) and small compared to the total well depth. Whilst Table 3 shows that there is some variation in the absolute well-depths from various ab initio calculations, the energy difference between the two lowest energy adducts is very consistent at (10.1 ± 0.4) kJ mol-1. In our subsequent MESMER analysis assessing the role of both adducts, the energy difference is fixed to our calculated value (10.1 kJ mol-1), but the absolute well depth of the C1 adduct is allow to float. The barrier for the abstraction reaction is calculated to be 3.6 kJ mol-1.

Figure 5. The potential energy diagram for the OH addition to isoprene. Relative energies were calculated at the CCSD(T)/CBS//M06-2X/6-311++G(3df,2p) level and include zero-point energy corrections.


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Table 3. Theoretically calculated well-depths for the isoprene + OH reaction with respect to the additions at carbons 1 and 4. All well-depths are corrected for zero-point energies

This work

154.1

144.0

Energy Difference between adducts/ kJ mol-1 10.1

Lei et al.46

145.6

135.1

10.5

Greenwald et al.47 Stevens et al.48

156.1 a

146.4

9.7

158.6

148.1

10.5

Peeters et al.14 163.2 a –including basis set correction at the roMP2 level of theory

153.6

9.6

Methodology

CCSD(T)/CBS//M06-2X/6311++G(3df,2p) CCSD(T)/6-311G**// B3LYP/6-31G roQCISD(T)/6-31++G**// B3LYP/6-311++G** PMP4-(SDTQ)/6-311G**// MP2/6-311G**+∆ZPE/ B3LYP/6-31G** CBS-APNO

Well-depth adduct C1 / kJ mol-1

Reference

Well-depth adduct C4 / kJ mol-1

The CCSD(T) method implemented in this work is known for accurately computing molecular properties and energies33, 38, 49 and is often referred to as “Gold Standard” of computational chemistry.50 Our calculated well-depth differs from that obtained by Lei et al.46 by 8.5 kJ mol-1, who have implemented a similar methodology. The use of smaller basis sets for the calculations of single point energies and structural optimizations as a computational constraint (6-311G** 51-58 and 6-31G56, 59-67 respectively) contributes to the observed well-depth discrepancy. London dispersion forces which are accounted for at the M06-2X level, and neglected by the B3LYP 68-71 functional also contribute to the discrepancy. Greenwald et al.47, have applied the restricted open-shell quadratic configuration interaction (CI) technique, with perturbative triple excitations33, 72 to study the isomeric branching of the isoprene + OH reaction. In this correlated method, quadratic terms are included in the configuration coefficients to correct for size consistency. The authors have done a very careful study when obtaining the stationary structures of the four possible isoprene-OH adducts. They have located 58 different local minima for the adducts at the B3LYP/6-311++G** level, and implemented the lowest energy conformations in subsequent roQCISD(T) computations. The roQCISD(T)/6-31++G**// B3LYP/6-311++G** methodology was validated against previous calculations on the ethylene-OH case, where the well-depth was calculated to within ~3.35 kJ mol-1.47, 73 They also report that the relative welldepths obtained at the PMP4(SDTQ)/6-311G**// B3LYP/6-311++G** level of theory are qualitatively aligned with those computed at the superior roQCISD(T)/6-31++G**//B3LYP/6-311++G** level. Stevens et al.48 have used the less computationally demanding fourth-order MøllerPlesset perturbation theory with single, double, triple and quadruple excitations and spin 15 ACS Paragon Plus Environment


projection (PMP4(SDTQ) to investigate the OH addition to isoprene. In the Møller-Plesset perturbation theory, the Hartree-Fock wavefunction is corrected for electron correlation by a combination with configurational functions, originated from single, double, triple, etc. excitations.74-75 In their study, PMP4-(SDTQ)/6-311G** single point energies computed for MP2/6-311G** optimized structures were subsequently corrected with zero-point energies calculated at the B3LYP/6-31G** level. Their calculations show a well-depth only 2.51 kJ mol-1 deeper than that reported by Greenwald et al. Peeters et al. have employed the Complete basis set method CBS-APNO76 to compute electronic energies while investigating the regeneration of HOx in the oxidation of isoprene.14 The authors have verified that the CBS-APNO method systematically overestimated the welldepth of the CH2=CH‒ĊH2 + O2 and for this reason, a correction of 4.18 kJ mol-1 have been applied. This fact suggests that the reported isoprene + OH well-depth might also be slightly overestimated by the CBS-APNO method.

4.2 Rate Coefficients for the OH + Isoprene Reaction, R1 Figure 2 shows an example of a typical experimental decay (inset) and bimolecular plot obtained at 406 K and 2 atm of nitrogen bath gas. Checks were carried out to ensure that the rate coefficients were invariant (within experimental error) of laser energy density (15 – 50 mJ cm-2) or repetition rate (1 – 10 Hz). Below 400 K, the addition of oxygen had no effect on the measured rate coefficient for reaction R1 as can be seen from Figure 2. Experiments in the presence of oxygen at temperatures > 450 K, where OH recycling was observed, will be presented in a subsequent publication focused on the validation of the LIM1 mechanism.15 A major issue when sampling the monitored species prior to detection, is whether the transit time from the sampling pinhole to detection influences the kinetic measurements. 18, 7779 In this study, room temperature pseudo-first-order rate coefficients of up to 70,000 s-1 are in excellent agreement with the literature data. At higher first order rate coefficients, the influence of transport can be observed, but can potentially be accounted for with a biexponential analysis.77 None of the measurements reported in this study required such corrections, i.e. transport is effectively instantaneous on the timescales of the chemical reaction. The analysis of the exponential decays is inset a few points to allow for the ~20 µs transport time. Figure 6 illustrates the observed temperature dependence of k1 from 298 – 794 K. In addition to varying the temperature, the pressure was also varied to ensure that measurements were always being made at the high pressure limit, i.e. that the observed bimolecular rate coefficients correspond to k1∞. No evidence for any pressure dependence was observed from 50 – 1670 Torr for the 298 – 650 K temperature range and these observations were consistent with the modelling discussed in the subsequent sections. Measurements performed at T ≥725 K are located in the fall-off region. For example, at 794 K, with k1a, 794K = (1.50 ± 0.63) × 10-11 cm3 molecule-1 s-1, our measurements are ~40% lower than our best estimate for k1a∞ at that temperature (2.49 × 10-11 cm3 molecule-1 s-1). Excellent 16 ACS Paragon Plus Environment

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agreement is observed between the measurements performed with the high and low-pressure instruments, as evidenced by the proximity of the black and blue triangles in Figure 6. A least-squares fit fit to the combined experimental data from both apparatus of the form k∞ 1 = A (

T 298 K

-n

) gives:

-11 k∞ 1 = (10.4 ± 0.4) × 10

T

-1.34 ± 0.12

298 K

cm3 molecule-1 s-1

E11

where errors are at the 2σ level. The negative temperature dependence is consistent with previous literature and is dominated by the addition reaction; however, this work considerably extends the range of temperatures studied. A full discussion on the values of k1 is presented in Section 4.5.

Figure 6. Comparison of experimental measurements using the high pressure instrument (black inverted triangles), measurements at the high pressure limit with a conventional low-pressure instrument (blue triangles) and at the fall-off region (red circles). The dotted line shows the IUPAC recommendation for the temperature dependence of the isoprene + OH reaction, the dashed line shows our best estimate for the high-pressure limit k1∞, which was obtained from a ME from this work and selected data as discussed in part c of this section. The continuous line represents k1∞ as obtained based purely on our measurements. Errors are statistical at the 2σ level.



As can be seen from Table 4, the room temperature rate coefficients for reaction R1 are in excellent agreement with the IUPAC recommendation and the bulk of the experimental literature providing evidence that the new apparatus works well and can generate reliable rate coefficients.


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Table 4. Comparison of Experimental Determinations of k1 Author/date

Technique

This work

LFPa – T = 298–630 K high p = 1290–1670 Torr pressure OH detection

This work

LFP/LIF

Conditions

T = 298–794 K p = 50–140 Torr

1010k1/cm3 molecule-1 s-1 at 298 K 0.99 ± 0.09

k1(T)/ cm3 molecule-1 s-1

(9.4 ± 0.2) × 10-11 298 K (9.7 ± 0.8) × 10-11 298 K -11

(2.0 ± 0.2) × 10

LFP/LIF Combined data

T = 298–794 K p = 50–1670 Torr

IUPAC (2013) Atkinson and Aschmann80 (1984) Atkinson et al.81 (1982) Campuzano-Jost et al. 82 (2000) Campuzano-Jost et al. 83 (2004) Chuong and

n/a

exp

298 K 527 ± 20

exp

1.00 ± 0.15 1.02 ± 0.04

RR

T = 299 K p = 735 Torr air T = 251–342 K p = 60–600 Torr T = 251–342 K p = 60–600 Torr T = 300–423 K

1.00 ± 0.05

DFf/LIF

c

c*

T -1.33 ± 0.32

(9.5 ± 1.2) × 10-11 298 K T

(1.8 ± 0.2) × 10-11 exp -11

2.7×10 exp(390±100/T)

0.856 ± 0.026

2.7×10-11 exp((336±74)/T)

0.847 ± 0.059

2.68×10-11 exp((348±136)/T)

1.10 ± 0.04

n/a 19


+ (1.3 ± 0.6) × 10-11 exp

-1.34 ± 0.12

T

n/a T = 295 K p = 760 Torr air

LFP/LIF

T -1.39 ± 0.56

(10.4 ± 0.4) × 10-11 298 K

Review RRe

LFP/LIF

RT

b

c

480 ± 58

522 ± 28

3

-3.61 kJ mol-1

1.06 ± 0.02 T -3.61 kJ mol-1 -11 -11 + (1.3 ± 0.6) × 10 exp (9.6 ± 0.2) × 10 b (t-butOOH) 298 K RT 1.04 ± 0.02 -1.38 ± 0.12 T (H2O2) (10.5 ± 0.4) × 10-11 c*

(1.8 ± 0.1) × 10 This work

+ (1.3 ± 0.6) × 10-11 exp

-1.10 ± 0.20

T

-11

d

-1.28 ± 0.71

T

T

-3.61 kJ mol-1

c* c*

RT

b

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Stevens21 (2000) Chuong and Stevens (2002)84 Dillon et al.22 (2017) Edney et al.85 (1986) Gill and Hites86 (2002) Hites and Turner87 (2009) Iida et al.88 (2002) Karl et al.89 (2004) Kleindienst et al.90 (1982) McGivern et al.19 (2000) McQuaid et al.91 (2002) Ohta 92 (1983) Park et al.93 (2004) Poppe et al.94 (2007) Singh and Li20 (2007) Vimal et al.95 (2008) Zhang et al.96

DF/LIF

LFP/LIF

p = 2–6 Torr He T = 300 K p = 100-150 Torr Ar

1.08 ± 0.05

T = 241–356 K 0.93 ± 0.04 p = 5–200 Torr (N2 or air) RR T = 297 K 1.01 ± 0.02 p = 1 atm air RR T = 298–363 K 1.01 ± 0.19 p = 1 atm He RR/MSg T = 323–413 K n/a p = 1 atm RR T = 298 K 1.04 ± 0.04 p = 760 Torr air GC / LIFh T = 294 K 1.00 ± 0.12 p = 760 Torr air FP/RF T = 297– 23 K 0.93 ± 0.15 p = 50–200 Torr Ar LFP/LIF T = 295 K 0.99 ± 0.05 p = 0.5–20 Torr Ar RR T = 298 K 1.11 ± 0.23 p = 760 Torr air RR T = 297 K 0.990 ± 0.027 p = 760 Torr air LFP/LIF T = 279 – 336 K 1.08 ± 0.19 p = 1-8 Torr LIF / MS / T = 295 K 1.02 ± 0.09 GCh p = 760 Torr RR/DF/ T = 240 – 340 1.04 ± 0.19 MS p = 1-3 Torr He DF / RF / T = 300 – 363 K 1.02 ± 0.06 LIF p = 2 –5 Torr He DF / MS T = 298 K 9.1

(1.93±0.08)×10-11 exp((446±12)/T)

2.54×10-11 exp((409±42)/T) 4.0×10-11 exp((249±20)/T)

2.36×10-11 exp((409±28)/T)

(3.49±0.46) ×10-11 exp((366±40)/T)

2.3×10-11 exp((444±27)/T)

20


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(2001) p = 1.9 Torr He Zhang et al.97 DF / MS T = 298 K 1.01 ± 0.08 (2000) p = 70–120 Torr N2 * – Measurements in the fall-off region (729 -794 K) were previously corrected to the high-pressure limit via Master Equation modelling. a – LFP = laser flash photolysis, b – Obtained from a Master Equation fit using the Trust region reflective algorithm98, c – Obtained from a simple non-linear least squares fit, d – LIF = laser induced fluorescence, e – RR = relative rate methodology RF = Resonance fluorescence, f – DF = discharge flow, g – MS = mass spectrometric detection, h – Chamber study where rate coefficients were fitted with experimental modelling. Uncertainties reported at 2σ for our data.

21



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4.3 The Abstraction Channel R1b From Figure 3, the fact that the green line fit (no abstraction) to the data is a much worse fit than the red line fit (with abstraction) is strong evidence that there is another loss process for OH in reaction R1. Abstraction is invoked to explain this behaviour as it is has been observed in many other OH + alkene reactions and our calculations predict an abstraction barrier consistent with both our observations and those of other studies, see below. A good example is the reaction between OH and C2H4, where the abstraction becomes measurably significant above 650 K, and is characterized with a (24.9 ± 1.2) kJ mol-1 barrier to abstraction.99-100 However, in the present system the barrier to H-abstraction at the CH3 group is expected to be much lower as the electron delocalization of the resulting allylic radical, C5H7, leads to resonant stabilization, absent in the ethylene case. The energy barrier of the allylic H abstraction from isoprene was theoretically explored with the aid of the Gaussian 09 D.01 software at the CCSD(T)/CBS//M06-2X/6-311++G(3df,2p) level of theory (see Figure 5). The calculated energetic barrier is equal to 3.6 kJ mol-1, consistent with an allylic abstraction having a lower barrier than a vinylic abstraction. As evidenced from the red line fit to the data in Figure 3, incorporation of abstraction, k1b, produces good fits to the experimental kinetic traces (also see global analysis traces, Figure 4). Abstraction reactions with barriers can be described using an Arrhenius description, and in the analysis of the equilibrium kinetic data - see Section 3.2 - the abstraction rate coefficient, k1b, was modelled with equation E10. It was noted that over the temperature range of the experiments k1b and E1b were not uniquely pinpointed; many sets of Arrhenius parameters could reproduce k1b. Therefore, in this data analysis E1b was fixed to our theoretical value, 3.6 kJ mol-1, and returned: k1b = (1.3 ± 0.6) × 10-11 exp

- 3.6 ± 3.5 kJ mol-1 RT

cm3 molecule-1 s-1.

E12

This fixed value of E1b provided the best fit to the data, but it is acknowledged other combinations of Arrhenius parameters can also provide an equally good fit to the data. As an exercise, E1b was floated, but bounded very close to our calculated value, so that essentially, the value is unchanged. The returned uncertainty 3.5 kJ mol-1 (2σ) provides an estimate of how well E1b is known. Using E12, k1 can be divided up into k1a and k1b for all the temperatures carried out in this study. Summaries of k1a and k1b are given in the SI, in Tables S.1 and S.2. While it is acknowledged that there are significant errors in extrapolating E12 to room temperature, the results suggest that ~3 ± 2% of the R1 occurs via abstraction at 298 K, k1b(298 K) = 3.1 × 10-12 cm3 molecule-1 s-1. Atkinson et al. have predicted negligible hydrogen abstraction from the OH + isoprene reaction at room temperature, with an estimate for the upper limit of the branching ratio of 1%.101 However, the ability of previous experiments to observe abstraction were probably not any better than 5%, so our present estimate of ~3% does not contradict previous studies. We note that OH abstraction from 3methyl-1-butene has been verified in a chamber study102 and product analysis reveals that the allylic H abstraction accounts for 5-10% of the overall OH reaction. Also, while no previous 22 ACS Paragon Plus Environment

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study has observed abstraction via R1, studies on the isoprene + Cl reaction indicate significant abstraction at room temperature (~15%).103-104 The stable product of Cl abstraction at the CH3 site, 2-methylene-3-butenal, was tentatively identified via atmospheric pressure ionization mass spectrometry.103 In our high pressure apparatus, the total pressure is considerably greater than 1 atmosphere. This means that it is straightforward to exhaust the reaction gas mixture from our time-resolved experiments into the proton-transfer mass spectrometer, where the stable products can be analysed; the transfer time is a few seconds. The peak related to the mass of 2-methylene-3-butenal (m/z = 83) was monitored in the 298-473 K temperature range, in the presence of [O2] (> 1 × 1018 molecule cm-3) to promote the oxidation of the potential allylic radical formed upon H abstraction. Figure 7 shows the variation of the m/z = 83 peak at room temperature, before and after the excimer laser is fired (5 Hz). Both the spectra were collected in the presence of H2O2, which means that when the laser is fired, the isoprene + OH chemistry is initiated. The observed promotion of peak m/z = 83 when the laser is fired corroborates the occurrence of abstraction via the allylic hydrogen. The promotion was also verified to be independent of isoprene concentration, which indicates that photolysis of isoprene is unlikely to be causing the observed effect.

Number of counts

1200 Laser OFF Laser ON

1000 800 600 400 200 0 71.0

71.2

Mass / Da

100

Number of counts

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Laser OFF Laser ON

80 60 40 20 0 82.8

83.0

Mass / Da

83.2

83.4

Figure 7. The change in the m/z = 83 at room temperature when the excimer laser is OFF (black line, no OH radicals generated) and ON (red line). [C5H8] = 5.3 × 1013 molecule cm-3, [O2] = 1.2 × 1019 molecule cm-3, T = 298 K, p = 1200 Torr.



The stable products of the addition channel, R1a, in the presence of O2 are expected to be methyl vinyl ketone and methacrolein, formed via HOC5H8O2 self-reaction.105 These products have identical mass and were observed with the proton-transfer mass spectrometer (m/z = 71) in much larger amounts compared to 2-methylene-3-butenal, see Figure 7. This result is evidence of direct abstraction, R1b, that is small, but not negligible at room temperature. The ratio of the peak areas (am/z = 83 / am/z = 71) ~ 0.07, is consistent with the reduced abstraction branching ratio if one assumes the molecules to have similar PTR-TOFMS sensitivities. 4.4 Interpretation of OH + Isoprene ⇌ Adducts Equilibria The isoprene molecule has four potential sites of OH addition as illustrated in Figure 5, however, a two-adduct model was adopted in the master equation (ME) calculations. Additions to the terminal carbons are believed to be dominant since they lead to the formation of stabilized allylic radicals.106 Additions at C1 and C4, which account together for more than 90% of the total additions93,106 were therefore selected for implementation in our analysis. A ME calculation including the four possible additions reveals that the equilibrium fractions of the radicals generated from additions to carbons 2 and 3, together, account for less than 0.1% at 729 K. The significant equilibrium fractions of adducts 1 and 4 (~65% and ~35% respectively) justifies that in our analysis only these two adducts are considered. In the analysis of the experimental data, see Section 3.2, only one well was considered when determining the adduct dissociation rate coefficient, (k-1a,expt). However, the current ME model considers two adducts (1 and 4). The two adduct model leads to tri-exponential OH decays, but to a very good approximation these decays can be modelled by a biexponential equation, and when fitted with equation E7, yields k-1a,calc. In the analysis the parameters of the ME are adjusted in order that k-1a,calc best fits k-1a,expt. This analysis means that both adducts are considered. Tests reveal that if the ME analysis had only considered adduct 1, the returned HOC5H8 binding energy would increase by approximately 2 kJ mol-1. The unimolecular coefficients k-1a,expt (see Table 2) were used to characterize the welldepths of the isoprene + OH reaction with the aid of the computational ME solver package MESMER42 and the numerical computing suite MATLAB R2016a107 via the Trust Region Reflective Algorithm.98 The logic is as follows: the ME was solved at the temperature and pressure of the experiments and generated an OH vs time profile, OH(t). This OH(t) was then passed to MATLAB where it is fitted to using equation E7, thus determining the calculated overall coefficient k-1a,calc. The parameters of the ME - binding energy, energy transfer for each bath gas M (Ad,M) and k1∞(T) were then adjusted by MATLAB in order to best fit k2 1a,calc to k-1a,expt, by minimizing the least-squares difference (χ ). The results are given in Table 5. In this analysis the well-depths for adducts 1 and 4 were adjusted in unison, maintaining their constant 10.1 kJ mol-1 difference, see Table 3. In the following discussion of the binding energy only adduct 1 is reported, as the energy of adduct 4 is simply 10.1 kJ mol-1 higher.


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Parameters obtained from a ME fit are dependent on the description of the molecular parameters (rotors, bends and vibrations) of the species involved in the reaction scheme. For example, the returned parameters are sensitive to the density of states of the reagents and adducts. This effect is evident when a vibration-only model is compared to a system where ten small harmonic vibrational frequencies of the reactants and products (≤ 350 cm-1) are replaced by the hindered rotor approximation (See Figure 1). The returned well-depth for addition at carbon 1 when the hindered rotors are used, (153.5 ± 6.2) kJ mol-1, is in excellent agreement with the theoretically calculated value at the -1 CCSD(T)/CBS//M06-2X/6-311++G(3df,2p) level (154.1 kJ mol ). However, the well-depth obtained with a less realistic vibration-only description of the system is significantly deeper, (166.5 ± 7.0) kJ mol-1. Differences between our experimentally determined well-depth and theoretical values obtained at the different levels of theory presented range from 0.6 to 9.7 kJ mol-1. Our best estimate of the binding energy, based purely on the measurements of this work is (153.5 ± 6.2) kJ mol-1 and is given in Table 5.

Table 5. Comparison of Experimental and calculated k-1a. Uncertainty at 1σ. T/K

k-1a,expt / s-1

k-1a,calc / s-1

Adduct 1 Welldepth / kJ mol-1

729 766 794

990 ± 870 3000 ± 2600 6500 ± 5500

1180 3160 6000

153.5 ± 6.2

The importance of the allylic hydrogen abstraction in the returned well-depths have also been explored in this investigation. If direct abstraction is neglected, then a unimolecular loss from the generic adduct presented in scheme S1 needs to be invoked (R3): k R

C5H8-OH Loss

(R3)

From Scheme S1, the solution is now given by k3 = k-1a + kR, where the slope of the slow decay of the equilibrium traces, λ-, is approximately equal to kR. If the abstraction route is supressed, i.e. k1b = 0, kR can provide an equally good fit to the data, but this reaction scheme skews k-1a, which is the crucial parameter required to assign the binding energy of the adduct, C5H8-OH. For instance, at the highest temperature, 794 K, the value of k-1a from Table 5 is 6500 ± 5500 s-1. However, if the highest temperature data are analysed with kR, the returned value for k-1a is 4810 ± 4200 s-1. This lower values of k-1a increases the binding energy of the adduct by 3.8 kJ mol-1. Even though we acknowledge that our experimental observations can be equally described using kR, we do not have evidence for R8. Our theoretical calculations have identified the direct abstraction channel, R1b, see Figure 5. In addition, R3 predicts negligible abstraction at room temperature but R1b predicts 3%; our proton transfer mass spectrometer observes the abstraction product at room temperature, see Figure 7 and Section 4.3. Therefore, the direct abstraction channel, R1b, is the favoured explanation of the slow decay, λ-. 25 ACS Paragon Plus Environment


Potential interference from radical-radical reactions (R+O2 does not happen to any extent at these high temperatures) could also contribute to OH loss from the equilibrium system, but is considered unlikely using the following reasoning. The typical precursor concentration employed in the more sensitive equilibrium experiments (~1 × 1014 molecule cm-3, calculated from OH removal in the absence of isoprene), the laser energy density (~15 mJ cm-2 or ~2 × 1016 photons cm-2), the precursor cross-section (~1 × 10-19 cm2 molecule-1 for H2O2) and the quantum yield, (2 for OH production from H2O2) is ~ 4 × 1011 molecule cm-3. If R + R is equal to 10-10 cm3 molecule-1 s-1 (upper limit) then this implies a k1b ~40 s-1, which is much lower than experimentally observed k1b. In some experiments with varying [OH] but similar [C5H8] and temperature, no significant change in the kinetic parameters were observed. Additionally, at T = 766 K the photolysis wavelength was changed to 266 nm (fourth harmonic from Quantel, Q-smart laser, ~ 10 mJ / pulse). Any minor photolysis of isoprene at 248 nm that could contribute to the radical pool and hence secondary chemistry, will be significantly reduced with this longer wavelength photolysis. The 266 nm data are wholly consistent with the other data, which is further evidence that little additional chemistry is occurring, other than that given by scheme S1.

4.5 Master Equation Modelling and Comparison with Literature In this section the master equation modelling package MESMER, described previously, has been used to compare various experimental values of k1 with a particular emphasis in determining the onset of pressure dependence. The complete data set of temperature and pressure dependent rate coefficients (187 values) from the references in Table 4 were fitted with the aid of MATLAB R2016a via the Trust Region Reflective Algorithm, in an analogous procedure to that described in the previous section. The only difference in the analysis that now MESMER also returns the forward isoprene + OH rate coefficients (k1a) to MATLAB. A 10% uncertainty was assigned for all the rate coefficients considered in this analysis. The fitting parameters were: the adduct well depth, Ad,M for the relevant bath gases used, and the high pressure limiting values of A1a, C1, A1a, C4 and n in the same format as equation E8. The pre-exponential factors for additions to carbons 1 and 4 were linked to maintain their constant ratio (A1a, C1 / A1a, C4 ~ 1.5).19 The vibrational and rotational constants of isoprene and the OH-C5H8 adducts were calculated at the M06-2X/6-311++G(3df,2p) level of 108 theory. Lennard Jones parameters were obtained from the work of Dibble et al. and Lei et al.46 A comparison of the complete experimental and fitted data is shown in Figure 8 and the resulting parameters are presented in Table 6. The proximity of most data points to the y = x line is expected from the IUPAC evaluation, where most studies are in excellent agreement. Three studies clearly stand out from the trend from this quantitative analysis; the low pressure measurements of Chuong and Stevens using discharge flow with OH detection by LIF, McGivern et al. using laser flash photolysis and LIF detection and the higher pressure LFP/LIF studies of Campuzano-Jost et al. Both of the low pressure measurements have been superseded by further, higher pressure measurements from the same research groups84, 93, 96 which are in good agreement with the 26 ACS Paragon Plus Environment

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IUPAC evaluation and the y = x line of this comparison. However, other low pressure, discharge flow/LIF studies from Stevens’ group, Vimal et al.95, at 363 K point to some potentially interesting properties of the OH/isoprene system in comparison to OH/butadiene at low pressures. Over the pressure range of 1-6 Torr of helium at 363 K, the OH + isoprene reaction is reported to show some pressure dependence (as does the study of Singh and Li under similar conditions), however, under identical conditions, the reactions of OH with the smaller butadiene and 1-butene molecules (which would be expected to demonstrate greater fall-off behaviour), show no pressure dependence. Vimal et al.95 used molecular dynamics simulations to investigate whether differences in the mechanism of internal energy distribution in isoprene and 1,3-butadiene could explain the lack of pressure dependence in 1,3 butadiene. Although their calculations suggested differences in the mechanisms of IVR between the two compounds, they reported that further studies were required to identify whether such differences in IVR mechanisms could account for the varying pressure dependence. Our ME simulations suggest that at 363 K, the high-pressure limit should be reached at 0.4 Torr of He.

1.4

k1a, Calc (T,p) / 10-10 cm3 molecule-1 s-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.2

1.0

0.8

0.6

0.4

0.2

0.0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

This work Kleindest et al. 1982 Campuzano-Jost et al. 2004 Campuzano-Jost et al. 2000 Chuong and Stevens 2000 Hites and Turner 2009 Singh et al. 2007 Park et al. 2004 McGivern et al. 2000 Atkinson 1982 Ohta et al. 1983 Atkinson and Aschmann 1984 Edney et al. 1986 McQuaid et al. 2002 Gill and Hites 2002 Chuong and Stevens 2002 Poppe et at. 2007 Zhang et al. 2001 Zhang et al. 2000 Vimal and Stevens 2008 Karl et al. 2004 Iida et al. 2002 Dillon et al. 2017

k1a, Exp (T,p) / 10-10 cm3 molecule-1 s-1

Figure 8. Correlation plot for experimental data points from all the data in Table 3 and the calculated rate coefficients generated by MESMER by allowing the well-depth, Ad,M, A and n to be floated. The resulting parameters are shown in the second column of Table 6.



The work of Singh and Li 20 reports a pressure dependence of

Page 28 of 40

k1 at 340 K over the 1 –

3 Torr pressure range of He. Their equivalent measurements of k∞ 1a at 1 and 2 Torr ((7.21 ± 0.65) × 10-11 and 8.16 × 10-11 cm3 molecule-1 s-1 respectively, corrected for abstraction with equation E12) are in good agreement with the set of selected studies presented previously, with ME predicted values of 7.92 × 10-11 and 7.98 × 10-11 cm3 molecule1 -1 s respectively. However, the rate coefficient measured at 3 Torr (9.26 × 10-11 cm3 molecule-1 s-1) is ~16% higher than what our calculations predict (8.00 × 10-11 cm3 molecule-1 s-1). Our simulations suggest that, in helium at 340 K, the high-pressure limit should be reached at 0.2 Torr. It is not easy to explain the discrepancy between the Campuzano-Jost et al.82-83 values and the remaining studies; Campuzano-Jost et al. recognised, but were unable to rationalize, the difference in their value of k1 and other literature data. A number of checks were carried out by Campuzano-Jost et al. but they were unable to identify the origin of the discrepancy. Given the high value of the rate coefficient k1, it is very unlikely that radical-radical processes could influence the OH decays and the invariance of the rate coefficients with photolysis laser power suggests such secondary chemistry plays no role in OH decays. Rate coefficients lower than the expected value can be an indication of recycling reactions,109-110 but the invariance of our measured rate coefficients at low temperatures with large concentrations of oxygen at least rules out oxygen leaks as a possible route to OH recycling in the CampuzanoJost et al. experiments. Given the good agreement in the temperature dependence of k1 with other measurements, the simplest explanation is some systematic error in determining isoprene concentrations in the reaction cell. That explanation is supported by the recent studies of Dillon et al.22 who determined UV absorption cross sections for isoprene which are approximately 10% greater than those of Campuzano-Jost et al. and in good agreement with another determination by Martins et al.111 Dillon et al. re-evaluated the Campuzano-Jost data using their new cross sections, generally bringing the Campuzano-Jost et al. data in closer agreement to the IUPAC evaluation. Removing the data sets from Campuzano-Jost et al., Chuong and Stevens, Vimal et al. and McGivern et al. produces a much better fit (as shown in Figure 9 and Table 6) with χ2 being reduced from 601.34 (~3.22 per point) for the complete data set to 56.53 for the selected data set of 115 data points (~0.49 per point). χ2 =0.49 implies that the data are on average within 6% of the fitted value. The resulting best fit parameters in the form of E8 are A1a = 9.52 ×10-11 cm3 molecule-1 s-1 and n1a∞ = -1.39. Studies represented in Figure 9 are the preferred ones (including this work), and are referred to as ‘Selected Data’. The returned parameters from the fittings where uncertainties were assigned as 10% of the measured coefficients are summarised in Table 6. It contains the returned parameters from considering the complete dataset and the selected data. While our k1a data at high temperatures, where equilibria is observed, has much larger than 10% error, it is consistent with the selected data, under this 10% error criteria.


Page 29 of 40

This work Kleindest et al. 1982 Hites and Turner 2009 Singh et al. 2007 Park et al. 2004 Atkinson 1982 Ohta et al. 1983 Atkinson and Aschmann 1984 Edney et al. 1986 McQuaid et al. 2002 Gill and Hites 2002 Chuong and Stevens 2002 Poppe et at. 2007 Zhang et al. 2001 Zhang et al. 2000 Karl et al. 2004 Iida et al. 2002 Dillon et al. 2017

1.4

k1a, Calc (T,p) / 10-10 cm3 molecule-1 s-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.0

0.2

0.4

0.6

k1a, Exp (T,p) / 10

0.8 -10

1.0

3

1.2 -1

cm molecule s

1.4

-1

Figure 9. Correlation plot for experimental data points from selected data in Table 4 (see text) and the calculated rate coefficients generated by MESMER by allowing the well-depth, Ad,M, A and n to be floated. The resulting parameters are shown in the ‘selected data’ column of Table 6.

The returned well-depth is virtually unaffected by which data are used as the well depth is almost exclusively determined by the high temperature data in this study. The other parameters associated with the fit: Ad,M , A1a and n1a are more dependent on the data set used. For each dataset used, fitted parameters are reported with either all possibilities of Ad,M floated or with some fixed. Varying the degree of flexibility in fitting Ad,M makes little difference to the returned values of A and ; these parameters are mainly dependent on the datasets considered in the analysis. The analysis was also performed with the use of a single-adduct model; the results for this case are also included in Table 7. Little variation is observed in the returned parameters, with the well-depths varying by 2.5 kJ mol-1. This small change is justified by the reduced equilibrium fraction of adduct 4 (~35%) compared to adduct 1 (~65%) and the small energetic difference to adduct 1 (~10 kJ mol-1). Finally, the last three columns of Table 7 shows results, including uncertainties, obtained from fits where the selected data was incorporated, and the uncertainties of our high temperature measurements (T > 720 K) were appropriately set as those of Table 2.


The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Page 30 of 40

Table 6. Returned parameters from MESMER fits to this work and the literature data using a two-adduct model and accounting for H abstraction with all data given an equal uncertainty of 10%. d,M = Ad,M × (T/298)mc -1

Well depth, E/kJ mol Ad / cm-1 He(m=1.00) Ar (m=0.50) N2 (m=0.25) A × 10 / cm3 molecule1 -1 s χ2 per point

153.1 150 (Fixed) 250 (Fixed) 200 (Fixed)

All Data 153.1 150 (Fixed) 250 (Fixed) 200

154.0 150 (Fixed) 250 (Fixed) 200 (Fixed)

Selected Data 153.6 150 (Fixed) 250 (Fixed) 150

152.9 100 250 190

153.6 100 100 150

8.32

8.33

8.34

9.55

9.52

9.52

-1.45 3.31

-1.45 3.31

-1.45 3.22

-1.44 0.56

-1.39 0.49

-1.39 0.49

Table 7. Returned parameters from MESMER fits to this work and the literature data and accounting for H abstraction with our higher temperature data given the uncertainties reported in Table 2. d,M = Ad,M × (T/298)m

Well depth, E/kJ mol-1 Ad / cm-1 He(m=1.00) Ar (m=0.50) N2 (m=0.25) A × 10 / cm3 molecule-1 s-1 χ2 per point

This work Two adduct model 153.7 ± 5.9 153.5 ± 6.2 n/a n/a n/a n/a 200 (Fixed) 150 ± 110

This work One adduct model (C1) 156.0 ± 3.9 156.0 ± 4.2 n/a n/a n/a n/a 200 (Fixed) 150 ± 70

153.6 ± 4.9 150 (Fixed) 250 (Fixed) 200 (Fixed)

153.4 ± 5.1 150 (Fixed) 250 (Fixed) 150 ± 90

153.2 ± 5.0 100 ± 350 100 ± 340 150 ± 90

9.53 ± 0.64

9.47 ± 0.65

9.46 ± 0.41

9.46 ± 0.42

9.46 ± 0.14

9.46 ± 0.14

9.47 ± 0.16

-1.35 ± 0.15 0.50

-1.33 ± 0.16 0.48

-1.33 ± 0.10 0.49

-1.32 ± 0.10 0.48

-1.34 ± 0.07 0.42

-1.33 ± 0.07 0.41

-1.33 ± 0.07 0.41

30


Selected Data

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4.6 Analytical Representation of Pressure and Temperature for k1a, k-1a,C1, and k-1a,C4 In order to provide analytical representations for the present master equation calculations, the output from our MESMER equations have been fitted using a Troe formalism: k1a T,M =

k1a,0 T M F x k1a,0 T M 1+ k∞ 1a T

E13

⊖ k-1a, C1(T,[M]) = k1a T,M × (RT)-1 × exp(∆H⊖ C1 /RT) × exp(-∆SC1 /R)

E14

⊖ k-1a, C4(T,[M]) = k1a T,M × (RT)-1 × exp(∆H⊖ C4 /RT) × exp(-∆SC4 /R)]

E15

where [M] is the concentration of the buffer gas, k1a,0 T is the low-pressure termolecular rate coefficient, k∞ 1a T is the high-pressure limit rate coefficient, and F(x) is the collision broadening factor. The collision broadening factor - F(x) - is calculated according to the formulation of Troe and Ushakov112, see Supporting Information. k-1a, C1 and k-1a, C4 are the decomposition rate coefficients for adducts 1 and 4, respectively, and are related to k1a via E14 and E15 using their thermodynamic parameters: ∆HC1, ∆SC1 and ∆HC4 ∆SC4. A global non-linear least-squares fit to the MESMER data using the Troe formalism was carried out, where k0 T and k∞ 1a T were defined according to equations E8a and E8b respectively. k0(T) = A0 × (T/298)n cm6 molecule-2 s-1 E8a k1a∞(T) = A1a × (T/298)m cm3 molecule-1 s-1

E8b

A0, A1a, n and m, and F(x)( FcentA, FcentB, !" and b), ∆HC1,C4 ∆SC1,C4 were adjusted to provide a good fit to the simulated pressure dependent coefficients k1a T,M . The results are given in Table 8, and these fits to the MESMER data are shown in Figure 10, where N2 was defined as the bath gas. Additional Troe fits where helium and argon were simulated as the buffer gases are also given in Table 8. Table 8. Troe fit parameters to MESMER-simulated rate coefficients, for N2, He, Ar. -11

3

-1

-1

A1a / 10 cm molecule s n A0 / 10-21 cm6 molecule-2 s-1 m b x0 FcentA FcentB -1 ∆H⊖ C1 / J mol ⊖ -1 -1 ∆SC1 / J mol K -1 ∆H⊖ C4 / J mol -1 -1 ∆S⊖ C4 / J mol K

N2

He

Ar

9.5 -1.26 1.68 -14.08 0.08 0.90 0.10 -0.0012 154043 108.9 147251 102.8

9.6 -1.30 1.10 -12.50 0.08 0.88 0.11 -0.0012 154308 109.3 147495 103.1

9.5 -1.30 1.43 -13.27 0.08 0.90 0.13 -0.0009 154512 109.6 147696 103.5



1E-10

k1a(T, p)

1E-11

300 K 400 K 500 K 600 K 700 K 800 K

1E-12

1E-13

1E-14 1013

1014

1015

1016

1017

1018

1019

1020

-3

log ([N2] / molecules cm ) 4

10

k-1a C1(T, p)

103 102 101 100 10-1 10-2 -3

10

1013

1014

1015

1016

1017

1018

1019

1020

1018

1019

1020

-3

log ([N2] / molecules cm ) 104 3

10

k-1a C4(T, p)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 40

102 101 100 10-1 10-2 -3

10

1013

1014

1015

1016

1017 -3

log ([N2] / molecules cm )

Figure 10. Fits of the Troe formalism to MESMER-simulated rate coefficients where N2 was implemented as the buffer gas at various temperatures. Markers represent MESMER-simulated rate coefficients and the lines of the same colour are the Troe fits to the data.


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5 Summary and Conclusions Measurements of the rate coefficient for the reaction of OH with isoprene, k1, made around room temperature using a new apparatus for high pressure studies are in good agreement with the extensive literature data, hence validating this new apparatus. Above ~700 K the OH temporal profiles exhibit biexponential behaviour, consistent with the establishment of the OH + C5H8 ⇌ adduct equilibrium. The experimental adduct dissociation data, k-1a, were fitted to using a master equation model where the adduct binding energy was adjusted. This analysis determined a well depth of (153.5 ± 6.2) kJ mol-1 for adduct 1, C1, and (143.4 ± 6.2) kJ mol-1 for adduct 4, C4. This value is in agreement with the present ab initio calculations (well depth for C1 adduct = 154.1 kJ mol-1) on the R1 potential energy surface. However, it is noted that the well depth determined from the experimental data is dependent on how the internal modes of reagents and adducts are treated, and only when the low vibrations are treated as hindered rotor does experiment and theory show agreement. The analysis of the > 700 K equilibrium data required an additional minor, but significant abstraction channel, R1b. Our ab initio calculations have identified this direct abstraction channel and the proton transfer mass spectrometer provides evidence that this channel is operating even at room temperature: k1b = (1.3 ± 0.3) × 10-11 exp

-3.61 kJ mol-1

RT

cm3

molecule-1 s-1. Our experimental data on reaction k1, together with the extensive literature data on this reaction, have been assessed using master equation analysis with the MESMER programme. This analysis indicates that there is no pressure dependence in the pressure range of the literature data, contradicting some previous studies. A selected dataset was then used to provide our recommended value for k1a(T,[M]). A Troe parametrization of k1a(T,[M]) provides an analytical form of our MESMER analysis. The temperature range for OH + isoprene studies has been significantly extended to ~800 K with -11 k∞ 1 = (9.5 ± 0.2) × 10

T 298 K

-1.33 ± 0.07

+ (1.3 ± 0.3) × 10-11 exp

-3.61 kJ mol-1

RT

.

Supporting Information Electronic supporting information is available containing experimental data, frequencies and structures from ab initio calculations, recommended partitioning between addition and abstraction as a function of temperature, Troe fits with He and Ar as third body, MESMER and Origin Scripts. Acknowledgements



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Kinetics of the Reaction of OH with Isoprene over a Wide Range of

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